Question: The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees Celsius) is modeled by: $P(x)=-2(x-9)^2+200$ What is the maximum number of fish?
Solution: The fish population is modeled by a quadratic function, whose graph is a parabola. The maximum number of fish is reached at the vertex. So in order to find the maximum number of fish, we need to find the vertex's $y$ -coordinate. The function $P(x)$ is given in vertex form. The vertex of $-2(x-{9})^2{+200}$ is at $({9},{200})$. In conclusion, the maximum fish population is $200$ thousand.